#include<bits/stdc++.h>
using namespace std;
#define f first
#define s second
typedef long long ll;
typedef long double ld;
typedef pair<int, pair<int, int>> ft;
const ld PI = acos(-1);
const int maxn = 3e3+5;
const ll inf = 1e18;
const int mod = 998244353;
int n, m, S, T, U, V;
ll ans = inf, stp;
ll ds[maxn], du[maxn], dv[maxn], dps[2][maxn], dpt[2][maxn];
int deg1[maxn], deg2[maxn], ing[maxn];
vector<pair<int, int>> graph[maxn];
vector<int> g1[maxn], g2[maxn];
void dijkstra(ll *d, int vt){
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
for(int i = 1; i <= n; i++){
d[i]=inf;
}
d[vt]=0;
pq.push({0, vt});
while(!pq.empty()){
auto x = pq.top();
//cout << x.f << "\n";
pq.pop();
if(d[x.s] < x.f)continue;
for(auto v: graph[x.s]){
if(x.f + v.s < d[v.f]){
d[v.f] = x.f+v.s;
pq.push({d[v.f], v.f});
}
}
}
}
signed main(){
cin >> n >> m >> S >> T >> U >> V;
while(m--){
int a, b, w;
cin >> a >> b >> w;
graph[a].push_back({b, w});
graph[b].push_back({a, w});
}
dijkstra(ds, S);
dijkstra(du, U);
dijkstra(dv, V);
queue<int> q;
q.push(T);
while(!q.empty()){
auto x = q.front();
q.pop();
if(ing[x])continue;
ing[x]=1;
for(auto v: graph[x]){
if(ds[v.f] + v.s == ds[x]){
g1[v.f].push_back(x);
g2[x].push_back(v.f);
deg1[x]++;
deg2[v.f]++;
q.push(v.f);
}
}
}
for(int i = 1; i <= n; i++){
dps[0][i] = dpt[0][i] = du[i];
dps[1][i] = dpt[1][i] = dv[i];
}
q.push(S);
while(!q.empty()){
auto x = q.front();
q.pop();
for(auto v: g1[x]){
dps[0][v] = min(dps[0][v], dps[0][x]);
dps[1][v] = min(dps[1][v], dps[1][x]);
deg1[v]--;
if(!deg1[v])q.push(v);
}
}
q.push(T);
while(!q.empty()){
auto x = q.front();
q.pop();
for(auto v: g1[x]){
dpt[0][v] = min(dpt[0][v], dpt[0][x]);
dpt[1][v] = min(dpt[1][v], dpt[1][x]);
deg2[v]--;
if(!deg2[v])q.push(v);
}
}
ans = du[V];
for(int i = 1; i <= n; i++){
if(ing[i]){
ans = min({ans, dps[0][i]+dpt[1][i], dps[1][i]+dpt[0][i]});
//cout << i << "\n";
}
}
cout << ans;
}
